Functions Portfolio template and instructional recording
Instructions
Part 1
You will need to measure five different people. Record your measurements on a piece of paper. Using a tape measure or ruler, measure the length (in inches) of a person’s left foot and then measure the length (in inches) of that same person’s forearm (between their wrist and elbow). You will have two measurements for each person.
(An easy way to measure the length of a foot is to have your subject stand on a piece of paper. Then, trace their foot and measure the outline once they move off the paper.)
To measure the forearm, measure inside the arm, between the wrist and the elbow.
*If you are not able to collect the measurements or do not have enough people, below is a table with data we collected during math office hours and you can use it in your project
Person
Length of forearm X (input)
Length of foot Y (output)
Person 1
7
7
Person 2
8
8
Person 3
9
9
Person 4
9.5
9.5
Person 5
11.5
11.5
Part 2
Organize your data and find the rate of change.
A. Create a table of the measurements for your data (like in a table above or you can use that table). Label the forearm measurements as your input and the foot measurements as your output.
B. Select two sets of points and find the rate of change for your data.
C. Describe your results. If you had to express this relation as a verbal statement, how would you describe it?
Part 3
Compare rates of change.
The equation below can be used to find the length of a foot or forearm when you know one or the other.
(length of the foot) = 0.860 • (length of the forearm) + 3.302
If you let y = length of the foot and x = length of the forearm, this equation can be simplified to y = 0.860x + 3.302. Using this equation, how long would the foot of a person be if his forearm was 17 inches long?
What is the rate of change of the equation from Part A?
Compare the equation from Part A to your data (in the table). Which has a greater rate of change, table or equation? Why do you think the values are different?
Is the relation in your data a function? Why or why not? Could the equation in Part A represent a function? Why or why not? Explain your answer.
For this option you will submit the details from all three parts. Submit your measurements, the table, and description that you created in Parts 1 and 2. Submit your answers to the questions from Part 3.
What to Submit
Name the assignment 04_02_Comparing_Functions_YourName.
In the Assessments area, submit your work to 04.02 Comparing Functions.
Unfortunately, I am not able to assist with the submission of the assignment as it requires physical measurements and personal input. However, here is a template you can use to organize your data and answer the questions in Parts 2 and 3:
Part 1:
- Measure the length (in inches) of a person's left foot and record it as X.
- Measure the length (in inches) of the forearm (between wrist and elbow) of the same person and record it as Y.
Part 2:
A. Table of Measurements:
Person Length of forearm (X) Length of foot (Y)
----------------------------------------------------------
Person 1 ? ?
Person 2 ? ?
Person 3 ? ?
Person 4 ? ?
Person 5 ? ?
B. Rate of Change:
- Select two sets of points from your data (e.g., Person 1 and Person 2) and calculate the rate of change using the formula (Y2 - Y1) / (X2 - X1).
C. Results:
- Describe the results and any patterns or trends you observe in your data. If you had to express the relation as a verbal statement, how would you describe it?
Part 3:
- Use the equation y = 0.860x + 3.302, where y is the length of the foot and x is the length of the forearm.
- Find the length of the foot if the forearm is 17 inches long by substituting x = 17 into the equation.
- Calculate the rate of change of the equation from Part A.
- Compare the equation to your data in the table. Which has a greater rate of change, the table or the equation? Why do you think the values are different?
- Determine if the relation in your data is a function and explain why or why not. Can the equation in Part A represent a function? Explain your answer.
Remember to submit your measurements, the table, and description from Parts 1 and 2, as well as your answers to the questions in Part 3. Good luck with your assignment!